The theory of dual groups

• Autorzy: A. Mekler , G. Schlitt
• Języki publikacji: EN

Abstrakty

EN

We study the $L_{∞, w}$-theory of sequences of dual groups and give a complete classification of the $L_{∞, w}$-elementary classes by finding simple invariants for them. We show that nonstandard models exist.

Kategorie tematyczne

• 03C75: Other infinitary logic
• 20K30: Automorphisms, homomorphisms, endomorphisms, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994
• Tom: 144
• Numer: 2
• Strony: 129-142

Daty

wydano

1994

otrzymano

1992-08-20

poprawiono

1993-06-24

Twórcy

autor

A. Mekler

• Department of Mathematics, University College of the Fraser Valley, 33844, King Rd., Abbotsford, British Columbia V2S 4N2, Canada

autor

G. Schlitt

• Department of Mathematics, University College of the Fraser Valley, 33844, King Rd., Abbotsford, British Columbia V2S 4N2, Canada

Bibliografia

• [1] J. Barwise, Back and forth through infinitary logic, in: Studies in Model Theory, MAA Stud. Math. 8, Math. Assoc. Amer., 1973, 5-34.
• [2] S. Chase, Function topologies on abelian groups, Illinois J. Math. 7 (1963), 593-608.
• [3] K. Eda and H. Ohta, On abelian groups of integer-valued continuous functions, their ℤ-duals and ℤ-reflexivity, in: Abelian Group Theory, Proc. Third Conf. Oberwolfach, Gordon & Breach, 1987, 241-257.
• [4] P. Eklof and A. Mekler, Almost Free Modules, North-Holland, 1990.
• [5] P. Eklof, A. Mekler and S. Shelah, On strongly-non-reflexive groups, Israel J. Math. 59 (1987), 283-298.
• [6] E. Ellentuck, Categoricity regained, J. Symbolic Logic 41 (1976), 639-643.
• [7] G. Reid, Almost Free Abelian Groups, lecture notes, Tulane University, unpublished, 1968.
• [8] G. Schlitt, Sheaves of abelian groups and the quotients A**/A, J. Algebra 158 (1993), 50-60.